1. Technical Field
A “directional lapped transform coder,” or “DLT Coder,” provides techniques for designing “directional lapped transforms,” and in particular, various techniques for performing lifting factorization of lapped transforms, with a “directional operator” then being applied in each lifting step to construct directional lapped transforms for use in coding signals of two or more dimensions.
2. Related Art
Typical block-based transforms, such as the well-known discrete cosine transform (DCT), have been widely used in image and video coding standards such as, for example, JPEG, MPEG-1/2/4, H.261/3/4, etc. In these coding standards, images are divided into small blocks on which the transform is applied. While such block-based schemes generally make the complexity of the transform low for most applications, blocking artifacts tend to increase in severity when the bit-rates are low. Furthermore, typical transform schemes do not exploit inter-block correlation. As a result, the coding efficiency of such transform schemes is not optimal.
As an alternative to block-based DCT-based schemes, the concept of “lapped transforms” is sometimes used. As is known to those skilled in the art, with lapped transforms, the transform blocks are overlapped. This overlapping allows lapped transforms to partially exploit inter-block correlations and reduce blocking artifacts significantly.
Various practical image coding schemes based on lapped transforms have demonstrated superior coding performance relative to traditional DCT-based image coding. Further, the computational complexity of lapped transform based coding schemes is not significantly greater than that of conventional DCT-based image coding. For example, compared to the well-known JPEG 2000 coding standard, which is based on wavelet transforms, one conventional lapped transform based scheme, referred to as “HD Photo,” provides comparable coding performance, but with lower complexity than JPEG 2000.
However, when applied in image or video coding, both 2D DCT and 2D lapped transforms are computed using two separable 1D transforms, i.e., horizontal and vertical transforms. In general, this type of separable design allows the transform to adequately capture both horizontal and vertical information. However, in typical images, there is no guarantee that that the information in those images is along the vertical or horizontal direction. Consequently, conventional separable transform based schemes tend not to adequately account for information that is not along one of the two directions.
On the other hand, conventional DCT generally approximates an optimal linear transform, such as the well-known Karhunen-Loève (KL) transform, given the assumption that the correlation of the signal is isotropic and strong. Unfortunately, this assumption is generally not true for most images, either natural or artificial. In particular, the correlation generally changes from region to region, and is likely to be stronger along some particular direction from region to region. However, this direction of strongest correlation is not necessarily horizontal or vertical.
Recently several conventional transforms have been proposed for use in image representation or image coding that provide directional bases. These directional schemes are generally classified into one of two categories. In the first category, new transforms are introduced to incorporate directional bases, like “curvelets,” and “dual tree complex wavelets.” The transforms of the second category are modified from the existing transforms. As is known to those skilled in the art, this second category includes “directional wavelet transforms” and “directional DCT transforms.”